Let’s set up the factors, with A and B being our unknown numbers:
5x^{2}+7x-6 =
(5x+A)*(x+B)

Expand and Simplify:
(5x+A)*(x+B) = 5x^{2} + 5Bx + Ax + AB
= 5x^{2} + (5B+A)x + AB

From here we can set up the comparisons:
5x^{2 }+ 7x - 6 = 5x^{2} + (5B+A)x + AB

7 = (5B+A)
-6 = AB

Let’s start with -6 = AB and find what product pairs work:
(1 and -6), (-1 and 6), (2 and -3), (-2 and 3), (3 and -2), (-3 and 2), (6 and -1), or (-6 and 1).

Now we plug in our (A and B) pairs above to see which one works for our other equation:
7 = (5B+A) = (A+5B)

For (1 and -6): 1 + 5(-6) = -29; no.
For (-1 and 6): -1 + 5(6) = 29; no.
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For (-3 and 2): -3 +5(2) = 7; yes!